auto_deriv: Tool for automatic differentiation of a Fortran code

Abstract
auto_deriv is a module comprised of a set of fortran 95 procedures which can be used to calculate the first and second partial derivatives (mixed or not) of any continuous function with many independent variables. The mathematical function should be expressed as one or more fortran 77/90/95 procedures. A new type of variables is defined and the overloading mechanism of functions and operators provided by the fortran 95 language is extensively used to define the differentiation rules. Proper (...

Title of program: AUTO_DERIV
Catalogue Id: ADLS_v2_0

Nature of problem
The need to calculate accurate derivatives of a multivariate function frequently arises in computational physics and chemistry. The most versatile approach to evaluate them by a computer, automatically and to machine precision, is via user-defined types and operator overloading. AUTO_DERIV is a Fortran 95 implementation of them, designed to evaluate the first and second derivatives of a function of many variables.

Versions of this program held in the CPC repository in Mendeley Data
ADLS_v1_0; AUTO_DERIV; 10.1016/S0010-4655(99)00513-5
ADLS_v2_0; AUTO_DERIV; 10.1016/j.cpc.2010.06.043

This program has been imported from the CPC Program Library held at Queen's University Belfast (1969-2019)

【摘要】auto_deriv是一组由Fortran 95子程序构成的模块，可用于计算任意多自变量连续函数的一阶、二阶偏导数（含混合偏导数）。待求的数学函数需以一个或多个Fortran 77/90/95子程序的形式给出。本模块定义了一种新型变量，并充分利用Fortran 95语言提供的函数与运算符重载（operator overloading）机制来构建求导规则。适当的（……）

程序标题：AUTO_DERIV
目录编号：ADLS_v2_0

问题背景
计算多变量函数的精确导数是计算物理与计算化学领域的常见需求。通过计算机自动计算并达到机器精度的最通用方法，是借助用户自定义类型（user-defined types）与运算符重载技术。AUTO_DERIV即为该方法的Fortran 95实现，专门用于计算多变量函数的一阶与二阶偏导数。

孟德尔莱数据（Mendeley Data）的CPC程序库中收录的该程序版本：
ADLS_v1_0；AUTO_DERIV；10.1016/S0010-4655(99)00513-5
ADLS_v2_0；AUTO_DERIV；10.1016/j.cpc.2010.06.043

本程序源自贝尔法斯特女王大学托管的CPC程序库（1969-2019年）

搜集汇总

背景与挑战

背景概述

该数据集描述了一个名为auto_deriv的Fortran 95工具，用于自动微分，能够计算多变量函数的一阶和二阶偏导数。它利用Fortran 95的运算符重载机制，提供精确的导数计算，主要应用于计算物理和化学领域，并包含两个版本的历史记录。